Revista Matemática Iberoamericana


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Volume 24, Issue 2, 2008, pp. 631–644
DOI: 10.4171/RMI/550

Notes on the roots of Steiner polynomials

Martin Henk[1] and María A. Hernández Cifre[2]

(1) Institut für Mathematik, Sekretariat MA 4-1, Technische Universität Berlin, Strasse des 17. Juni 137, 10623, BERLIN, GERMANY
(2) Departamento de Matemáticas, Universidad de Murcia, Campus Universitario de Espinardo, 30100, MURCIA, SPAIN

We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the in- and circumradius of the convex body. We show that the roots of 1-tangential bodies fulfill the conjecture, but we also present convex bodies violating each of the conjectured properties.

Keywords: Steiner polynomial, Teissier’s problem, tangential bodies, circumradius, inradius

Henk Martin, Hernández Cifre María: Notes on the roots of Steiner polynomials. Rev. Mat. Iberoamericana 24 (2008), 631-644. doi: 10.4171/RMI/550